Kategoriarkiv: Calculus

Vectorproducts

Vectors can be multiplied in two ways: 1. The scalar product gives product of a vector and the projection of  the other vector upon the first one. This is calculated according to a b = ab cos(v) The result is a … Fortsätt läsa

Publicerat i Calculus, Uncategorized | Märkt , | 2 kommentarer

Numerical methods for calculation of integrals

For many functions it is impossible to find a primtive function and therefore it is impossible to use the fundamental theorem of calculus to solve the integral. Luckily there are ways to cope with such circumstances with the aid of … Fortsätt läsa

Publicerat i Calculus, matematik 5 | Märkt | Lämna en kommentar

Symmetries, translations and dilatations

A good definition of symmetry was given by the mathematician Hermann Weyl:  An object is symmetrical  if, after you performed an operation on it, it still looks the same as it did before. A function can be moved in the … Fortsätt läsa

Publicerat i Calculus, Gymnasiematematik(high school math), Uncategorized | Lämna en kommentar

Properties of integrals

 the integral of a linear combination is the linear combination of the integrals, If a > b then define 3. Additivity of integration on intervals. If c is any element of [a, b], then 4. Upper and lower bounds. An … Fortsätt läsa

Publicerat i Calculus, matematik 3c, matematik 4 | Märkt | Lämna en kommentar

Definite integrals

In a geometrical context the integral can be interpreted as the area between the graph of the integrand f(x) and the x-axis. The idea is to summarize infinitely many infinitely thin rectangles. (An alternative approach to areacomputation is the Lebesgue-integration where you … Fortsätt läsa

Publicerat i Calculus, Gymnasiematematik(high school math), matematik 3c, matematik 4 | Märkt | 1 kommentar

Indefinite integrals

If you need to calculate the distance travelled when you know the velocity as a function of time , since s'(t) = v(t) you need to be able to perform antiderivation i.e. finding a function whose derivative equals your function. … Fortsätt läsa

Publicerat i Calculus, Gymnasiematematik(high school math), matematik 3c, matematik 4 | Märkt , | Lämna en kommentar

Differentiating the natural logarithm, products and quotients

In order to be able to deduce the derivative of the natural logarithm we resort to using implicit differentiation. Let x= ey(x) Differentiating both sides gives dx/dx = d ey(x)/dx 1=ey(x) dy(x)/dx Solving for dy(x)/dx one obtains dy(x)/dx = 1/ey(x) … Fortsätt läsa

Publicerat i Calculus, Gymnasiematematik(high school math), matematik 3c, matematik 4 | Märkt , , | Lämna en kommentar

Differentiation of the trigonometric functions

To be able to differentiate the trigonometric functions one needs some standard limits: With the aid of these and the definition of the derivative it is possible to show that f(x)= sin (x) implies  f ‘(x) = cos(x) and f(x) … Fortsätt läsa

Publicerat i Calculus, Gymnasiematematik(high school math), matematik 4 | Märkt | Lämna en kommentar